Top 50 DP Problems
Dynamic Programming problems are among the most challenging but rewarding in interviews. They test your ability to identify overlapping subproblems and optimal substructure.
Essential DP Problems:
- Fibonacci (memoization & tabulation)
- Climbing Stairs
- Coin Change (minimum coins)
- Coin Change II (number of ways)
- 0/1 Knapsack
- Unbounded Knapsack
- Longest Increasing Subsequence
- Longest Common Subsequence
- Edit Distance
- Minimum Path Sum (grid DP)
- Unique Paths (grid DP)
- House Robber (I, II, III)
- Maximum Product Subarray
- Word Break
- Decode Ways
- Partition Equal Subset Sum
- Target Sum
- Burst Balloons
- Longest Palindromic Subsequence
- Palindrome Partitioning II
Strategies:
- Start with recursion, then add memoization.
- Identify dimensions of state (index, remaining capacity, etc.).
- Draw the DP table to visualize transitions.
- Optimize space by noticing only previous rows are needed.
Example: Coin Change (minimum coins)
public int coinChange(int[] coins, int amount) {
int[] dp = new int[amount + 1];
Arrays.fill(dp, amount + 1);
dp[0] = 0;
for (int i = 1; i <= amount; i++) {
for (int coin : coins) {
if (i >= coin) {
dp[i] = Math.min(dp[i], dp[i - coin] + 1);
}
}
}
return dp[amount] > amount ? -1 : dp[amount];
}
Two Minute Drill
- DP problems require careful state definition and transition.
- Practice both top-down memoization and bottom-up tabulation.
- Understand classic problems thoroughly; variations often appear.
- Time complexity is often O(n²) or O(n*amount).
Need more clarification?
Drop us an email at career@quipoinfotech.com